If you are trying to change the iCloud account to your current ID, and if the old ID is an earlier version of your current ID, temporarily recreate the old ID by going to https://appleid.apple.com, click Manage my Apple ID and sign in with your current iCloud ID. Click edit next to the primary email account, change it back to your old email address and save the change. Then edit the name of the account to change it back to your old email address. You can now use your current password to turn off Find My iDevice, even though it prompts you for the password for your old account ID. Then save any photo stream photos that you wish to keep to your camera roll. When finished go to Settings>iCloud, tap Delete Account and choose Delete from My iDevice when prompted (your iCloud data will still be in iCloud). Next, go back to https://appleid.apple.com and change your primary email address and iCloud ID name back to the way it was. Now you can go to Settings>iCloud and sign in with your current iCloud ID and password.
Note: this will not work if your current ID is an entirely new ID that was never previously associated with the old email address. If that's the case, you'll need to contact the Apple account security team for your country for assistance resetting the password for the old ID: http://support.apple.com/kb/HT5699.